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In ARIMA(p, d, q), p represents the number of autoregressive (AR) terms, d is the number of first differences applied to make the data stationary, and q denotes the number of moving average (MA) terms.

Conditions: Applies to ARIMA model notation.

In ARIMA(p, d, q), p represents the number of autoregressive (AR) terms, d is the number of first differences applied to make the data stationary, and q denotes the number of moving average (MA) terms.

Conditions: Applies to ARIMA model notation.

Differencing is a technique used to transform a non-stationary time series into a stationary one by computing the differences between consecutive observations.

Conditions: Used when data exhibits non-stationarity.

Differencing is a technique used to transform a non-stationary time series into a stationary one by computing the differences between consecutive observations.

Conditions: Used when data exhibits non-stationarity.

Stationarity means that the statistical distribution of the data depends only on the difference in time between observations, rather than their absolute location in time.

Conditions: Applies to time series data.

Stationarity means that the statistical distribution of the data depends only on the difference in time between observations, rather than their absolute location in time.

Conditions: Applies to time series data.

An ARIMA(1,1,1) model consists of taking a first difference of the original series and then fitting an ARMA(1,1) model to the resulting differenced series. The equations are $Y_t - Y_{t-1} = W_t$ and $W_t = \omega + \phi_1 W_{t-1} + \theta_1 e_{t-1} + e_t$.

Conditions: $p=1$ (one AR term); $d=1$ (one first difference); $q=1$ (one MA term)

An ARIMA(1,1,1) model consists of taking a first difference of the original series and then fitting an ARMA(1,1) model to the resulting differenced series. The equations are $Y_t - Y_{t-1} = W_t$ and $W_t = \omega + \phi_1 W_{t-1} + \theta_1 e_{t-1} + e_t$.

Conditions: $p=1$ (one AR term); $d=1$ (one first difference); $q=1$ (one MA term)